Question

The base of a triangle is 1 cm more than the height. If the area is 10 cm², find the base and the height.

Part 1 of 2
What is the base of the triangle?

What is the height of the triangle?

Answer 1

• Base of triangle = 5 cm
• Height of triangle = 4 cm.

Explanation:

It's given that, The base of a triangle is 1 cm more than the height

Let's assume height of the triangle be x and base of the triangle be 1 + x

Also the area of the triangle is 10 cm².

We know that area of triangle is calculated by,

• Area = 1/2 × Base × height

Putting the values we get ,

`(1)/(2) (1 + x) x = 10 \\ \\ (1 + x)x = 10 * 2 \\ \\ {x}^(2) + x = 20 \\ \\ {x}^(2) + x - 20 = 0`

Further solving by factorisation,

`x^2 + x-20 = 0 \\ \\ x^2 +5x-4x - 20 = 0 \\ \\ x(x+5)-4(x+5)= 0 \\ \\ (x-4) (x+5) = 0 \\ \\ (x-4) = 0 \: or \: (x+5)=0 \\ \\ { \underline{x= 4 \: or \: x = 5 }}`

Since value can't be negative.

So, x = 4.

Hence, height of triangle x = 4 cm

base of triangle = x + 1

= 4 + 1

= 5 cm

Therefore the Base of traingle will be 5 cm and Height of the triangle will be 4 cm.