Question

Question 9
The base and the height of a triangle are in the ratio 5:3. If the area of the triangle is 67m^2.find
its base and height.​

Answer 1

Solution

Given:-

• The base and the height of a triangle are in the ratio 5:3
• Area of rhe triangle =67 m²

Find :-

• Base & Height of triangle

Explanation

Using Formula

$\dag\boxed{\underline{\tt{\red{\:Area_{triangle}\:=\:\dfrac{(Base)\times(Height)}{2}}}}}$

Let,

• Base = x
• Height = y,

Case 1.

==> x : y = 5:3

==> x/y = 5/3

==> 3x - 5y = 0 _________(1)

Case 2.

==> Area of triangle = (x).(y)/2

==> 67 = xy/2

==> xy = 67×2

==> xy = 134 _____________(2)

By, Equ(1)

==> x = 5y/3 _____________(3)

Keep in equ(2)

==> (5y/3).y = 134

==> y² = 134×3/5

==> y² = 402/5

==> y² = 80.4

==> y = √(80.4)

==> y = 8.97 m

Keel in equ(3)

==> x = 5 × 8.97/3

==> x = 44.85/3

==> x = 14.95

Hence

• Base of triangle = 14.95 m
• Height of triangle = 8.97 m

____________________