Question

26. The base of a triangle is 8 cm less than twice
re
its height. If the area of the triangle be 320
d
sq. cm, find its height.​

Answer 1

• Given

• Base of a triangle is 8 cm less than twice its height.
• Area of the triangle = 320 sq.cm

• To find

• Height of the triangle

• Concept

• Firstly, we will let the height of the triangle be x and the base of the triangle be 2x - 8. (As mentioned in the question the base is 8cm less than twice the breadth.)

• We have the value of the area of the triangle = 320 cm²

• So, by using the formula of area of triangle we will find the value of x and then by substituting the value of x in height. We will find its value.

• Solution

Let the height be x cm and the breadth be 2x - 8 cm.

Using formula,

Area of triangle = 1/2 × b × h

Where,

• b = base of the triangle
• h = height of the triangle

Substituting the values,

⟶ 320 = 1/2 × (2x - 8) × x

⟶ 320 × 2 = (2x - 8) x

⟶ 640 = 2x² - 8x

⟶ Take 2 common from both the sides.

⟶ 2(320) = 2(x² - 4x)

⟶ Cancel 2.

⟶ 320 = x² - 4x

⟶ x² - 4x - 320 = 0

⟶ x² - 20x + 16x - 320 = 0

⟶ x(x - 20) + 16(x - 20) = 0

⟶ (x + 16) (x - 20) = 0

⟶ x = - 16 Reject - ve

⟶ x = 20

The value of x = 20

Base of the triangle = 2x - 8 = 2 × 20 - 8 = 40 - 8 = 32 cm

Height of the triangle = x = 20 cm