Chapter 11, Problem 3MPS

To determine

To find: The height and if the problem has no solution give explanation.

Answer to Problem 3MPS

The height of triangle is $12\text{cm}$ .

Explanation of Solution

Given information:

Base of first triangle is $18\text{cm}$ , height is $10\text{cm}$ .

The base of second triangle is $15\text{}\text{cm}$ .

Area of both triangles is same.

Calculation:

The area of area of first triangle is calculated as,

  $A_1=\frac{1}{2}{b}_1{h}_1$

Area of second triangle is calculated as,

  $A_2=\frac{1}{2}{b}_2{h}_2$

Since, the area of both triangles is same it can be written as,

  $\frac{1}{2}{b}_1{h}_1=\frac{1}{2}{b}_2{h}_2$ .

Substitute the values in above equation.

  $\begin{array}{l}\frac{1}{2}\left(18\text{cm}\right)\left(10\text{cm}\right)=\frac{1}{2}\left(15\text{cm}\right)h_2\\ h_2=\frac{\left(18\text{cm}\right)\left(10\text{cm}\right)}{15\text{cm}}\\ h_2=12\text{cm}\end{array}$

Therefore, the height of triangle is $12\text{cm}$ .