# The sides of a triangular plate are $8cm$,$15cm$and$17cm$.If its weight is $96gm$,find the weight

of the plate per square $cm$.

$\left( A \right)$.$1.6gm$

$\left( B \right)$.$0.8gm$

$\left( C \right)$.$1.4gm$

$\left( D \right)$.$2gm$

Last updated date: 22nd Mar 2023

•

Total views: 307.2k

•

Views today: 7.85k

Answer

Verified

307.2k+ views

Hint: Use Heron’s formula to compute the area of the triangular plate and find weight per square cm by dividing the weight by area of the triangle.

Let $ABC$be the triangular plate with sides

$

AB = 17cm \\

AC = 15cm \\

BC = 8cm \\

$

Given the problem, the weight of this triangular plate is $w = 96gm$.

In order to find the weight of the plate per square $cm$, we first need to compute the area of the

same.

Since sides of the triangular plate are given, we can use Heron’s formula to calculate the area of the

plate.

Heron’s formula states that area of the triangle is given by,

\[\Delta = \sqrt {s\left( {s - a} \right)\left( {s - b} \right)\left( {s - c} \right)} {\text{ (1)}}\]

In the above equation, $s$ is the semi-perimeter of the triangle and $a,b,c$ are the sides of the

triangle.

Sides of the triangular plate $ABC$are given by

$\left(

a = AB = 17cm \\

b = BC = 8cm \\

c = AC = 15cm \\

\right){\text{ (2)}}$

Semi-perimeter of triangle $ABC$ is given by,

$

s = \dfrac{{a + b + c}}{2} \\

\Rightarrow s = \dfrac{{17 + 8 + 15}}{2} = 20cm{\text{ (3)}} \\

$

Using equation $(2)$and $(3)$ in $(1)$,we get

\[

\Delta = \sqrt {20\left( {20 - 17} \right)\left( {20 - 8} \right)\left( {20 - 15} \right)} \\

\Rightarrow \Delta = \sqrt {20\left( 3 \right)\left( {12} \right)\left( 5 \right)} = 60c{m^2} \\

\]

Therefore, weight of the triangular plate per square $cm = \dfrac{w}{\Delta } =

\dfrac{{96gm}}{{60c{m^2}}} = 1.6gm$per $c{m^2}$.

Hence the correct option is $\left( A \right)$.$1.6gm$ .

Note: Heron’s formula should be used to compute the area where sides of the triangle are given. In

the problems like above, units need to be mentioned in the final answer.

Let $ABC$be the triangular plate with sides

$

AB = 17cm \\

AC = 15cm \\

BC = 8cm \\

$

Given the problem, the weight of this triangular plate is $w = 96gm$.

In order to find the weight of the plate per square $cm$, we first need to compute the area of the

same.

Since sides of the triangular plate are given, we can use Heron’s formula to calculate the area of the

plate.

Heron’s formula states that area of the triangle is given by,

\[\Delta = \sqrt {s\left( {s - a} \right)\left( {s - b} \right)\left( {s - c} \right)} {\text{ (1)}}\]

In the above equation, $s$ is the semi-perimeter of the triangle and $a,b,c$ are the sides of the

triangle.

Sides of the triangular plate $ABC$are given by

$\left(

a = AB = 17cm \\

b = BC = 8cm \\

c = AC = 15cm \\

\right){\text{ (2)}}$

Semi-perimeter of triangle $ABC$ is given by,

$

s = \dfrac{{a + b + c}}{2} \\

\Rightarrow s = \dfrac{{17 + 8 + 15}}{2} = 20cm{\text{ (3)}} \\

$

Using equation $(2)$and $(3)$ in $(1)$,we get

\[

\Delta = \sqrt {20\left( {20 - 17} \right)\left( {20 - 8} \right)\left( {20 - 15} \right)} \\

\Rightarrow \Delta = \sqrt {20\left( 3 \right)\left( {12} \right)\left( 5 \right)} = 60c{m^2} \\

\]

Therefore, weight of the triangular plate per square $cm = \dfrac{w}{\Delta } =

\dfrac{{96gm}}{{60c{m^2}}} = 1.6gm$per $c{m^2}$.

Hence the correct option is $\left( A \right)$.$1.6gm$ .

Note: Heron’s formula should be used to compute the area where sides of the triangle are given. In

the problems like above, units need to be mentioned in the final answer.

Recently Updated Pages

If ab and c are unit vectors then left ab2 right+bc2+ca2 class 12 maths JEE_Main

A rod AB of length 4 units moves horizontally when class 11 maths JEE_Main

Evaluate the value of intlimits0pi cos 3xdx A 0 B 1 class 12 maths JEE_Main

Which of the following is correct 1 nleft S cup T right class 10 maths JEE_Main

What is the area of the triangle with vertices Aleft class 11 maths JEE_Main

KCN reacts readily to give a cyanide with A Ethyl alcohol class 12 chemistry JEE_Main

Trending doubts

What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

Name the Largest and the Smallest Cell in the Human Body ?