Question

the base and height of a triangle are in the ratio 4:5 if the area of the triangle is 90 sq m find measure of its base and height​

Answer 1

Answer:

base = 36 m

height = 45 m

Step-by-step explanation:

let the base and height be 4x and 5x

ATQ, 1/2*4X*5x = 90

=> 10x = 90

=> X = 90/10

=> x = 9

4*9 = 36

5*9 = 45

Answer 2

Given:

A triangle with

• Ratio of base and height = 4:5
• Area = 90 sq.m

What To Find:

We have to find the

• Base
• Height

How To Find:

To find base and height, we have to

• Take x as the common multiple in the ratio 4 : 5 = 4x : 5x
• Use the formula - $\sf{Area = \dfrac{1}{2} \times Base \times Height}$
• Where Base = 4x and height = 5x

Solution:

Using the formula,

⇒ $\sf{Area = \dfrac{1}{2} \times Base \times Height}$

Substitute the values,

⇒ $\sf{90 \: sq.cm = \dfrac{1}{2} \times 4x \times 5x}$

Mutiply 1, 4x and 5x,

⇒ $\sf{90 \: sq.cm = \dfrac{20x}{2}}$

Take 2 to LHS,

⇒ $\sf{90 \times 2 = 20x}$

Multiply 90 by 2,

⇒ 180 = 20x

Take 20 to LHS,

⇒ $\sf{\dfrac{180}{20} = x}$

Cancel the zeros,

⇒ $\sf{\dfrac{18\!\!\!\not0}{2\!\!\!\not0} = x}$

Divide 18 by 2,

⇒ 9 cm = x

Now, substitute the value,

• Base = 4x = 4 × 9 = 36 cm
• Height = 5x = 5 × 9 = 45 cm

∴ Thus, the base is 36 cm and the height is 45 cm.