Question

The areas of squares drawn on the sides of a right-angled triangle of side length 13cm, 12cm and 5cm will be equal to: (Follow the order of sides to answer the areas of each square )
(a) 144 sq. cm., 169 sq. cm., 125 sq. cm.
(b) 169 sq. cm., 144 sq. cm., 25 sq. cm.
(c) 126 sq. cm., 144 sq. cm.,169 sq. cm.
(d) 144 sq. cm., 169 sq. cm., 25 sq. cm.

Answer 1

Hint: Use the formula that the area of a square is the square of its side.
i.e. Area of a square $={{\left( side \right)}^{2}}$. One by one, put the lengths of the sides of the right angled triangle in order in this formula to get the final answer.

Complete Step-by-step answer:
In this question, we are given that squares are drawn on the sides of a right-angled triangle of side length 13cm, 12cm and 5cm.
We draw the following diagram to understand the situation better:

We need to find the areas of these squares.
We already know the formula that the area of a square is the square of its side.
i.e. Area of a square $={{\left( side \right)}^{2}}$
The hypotenuse is the biggest side of the right angled triangle. It is 13 cm long. The square drawn on hypotenuse with side length 13 cm will have an area of ${{13}^{2}}=169$ sq. cm.
Hence, area of Square drawn on Hypotenuse = 169 sq. cm.
Now, let the side with length 12 cm be the base of the right angled triangle.
The square drawn on base with side length 12 cm will have an area of ${{12}^{2}}=144$ sq. cm.
Hence, area of Square drawn on base = 144 sq. cm.
Now, let the side with length 5 cm be the altitude of the right angled triangle.
The square drawn on altitude with side length 5 cm will have an area of ${{5}^{2}}=25$ sq. cm.
Hence, area of Square drawn on base = 25 sq. cm.
Hence, the areas of squares drawn on the sides of a right-angled triangle of side length 13cm, 12cm and 5cm will be equal to 169 sq. cm., 144 sq. cm., 25 sq. cm.
So, option (b) is correct.

Note: In this question, it is very important to know the formula that the area of a square is the square of its side. i.e. Area of a square $={{\left( side \right)}^{2}}$. Take care of the order in which you have to give the answer as you can make mistakes in that.