Question

Each side of triangle is increased by 10 cm. if the ratio of the perimeter of a new triangle is 5:4.find the perimeter of the given triangle

Answer 1

ANSWER:

Given:

• Each side of triangle is increased by 10cm.
• Ratio of perimeter of the new triangle to the original one is 5:4.

To Find:

• Perimeter of the original triangle.

Solution:

⇒ Perimeter = Sum of all sides of a triangle.

⇒ Perimeter of the original triangle = (x + y + z)cm

Here, x,y, and z are the sides of the triangle.

⇒ Perimeter of the new triangle = [(x+10)+(y+10)+(z+10)]cm

We are given that,

$:\implies \text{Perimeter of new triangle} : \text{Perimeter of original triangle} = 5 : 4 \\\\:\implies \dfrac{\text{Perimeter of new triangle}}{\text{Perimeter of original triangle}} = \dfrac{5}{4} \\\\:\implies \dfrac{[(x+10)+(y+10)+(z+10)]}{(x+y+z)} = \dfrac{5}{4} \\\\:\implies \dfrac{(x+y+z+30)}{(x+y+z)} = \dfrac{5}{4} \\\\:\implies 4(x+y+z+30) = 5(x+y+z) \\\\:\implies 4(x+y+z) + 120 = 5(x+y+z) \\\\:\implies 5(x+y+z) - 4(x+y+z) = 120 \\\\:\implies x + y + z = 120cm \\\\\bf{:\implies \text{\bf{Perimeter of the original triangle}}= 120cm}$