: The perimeter of an isosceles triangle is 90 m. If the length of the two equal sides is $\dfrac{3}{4}$ of the length of the unequal side, find the dimensions of the triangle.
Answer
Verified
Hint: With the given perimeter ,we can form a linear equation with two variables and by solving it we get the dimensions of the triangle.
Complete step-by-step answer: Step 1: It is given that it is an isosceles triangle. In an isosceles triangle any two sides are equal . We are given the perimeter of the triangle and we know that the perimeter of the triangle is just the sum of its three sides.
Step 2 :
Let the length of the sides be x , y , z. Perimeter = x+y+z Since it is an isosceles triangle, x = y Therefore , perimeter = x + x +z $ \Rightarrow 90 = 2x + z$………….(1) Step 3: It is given that the length of the two equal sides is $\dfrac{3}{4}$ of the length of the unequal side. $ \Rightarrow x = \dfrac{3}{4}z$ Cross multiplying we get $ \Rightarrow 4x = 3z \\ \Rightarrow \dfrac{4}{3}x = z \\ $ Now lets substitute the above value in equation (1) $ \Rightarrow 90 = 2x + \dfrac{4}{3}x$ Taking LCM , we get $ \Rightarrow 90 = \dfrac{{6x + 4x}}{3}$ Cross multiplying we get, $ \Rightarrow 270 = 10x \\ \Rightarrow \dfrac{{270}}{{10}} = x \\ \Rightarrow x = 27m \\ $ Now we have obtained the value of x and as it is an isosceles triangle y = 27 m Step 4 : To find the value of z , substitute the value of x in equation (1) $ \Rightarrow 90 = 2(27) + z \\ \Rightarrow 90 = 54 + z \\ \Rightarrow 90 - 54 = z \\ \Rightarrow z = 36m \\ $ Therefore the value of z=36m
Therefore, the dimensions of the isosceles triangle are 27 m , 27 m , 36 m.
Note: In this problem we have used a substitution method to solve the linear equation but we can also use elimination method to solve them.
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