Question

the height of a triangle is 7 cm longer than its base. The area of the triangle is 60 cm². What is the base of the triangle?

Answer 1

Answer:

the base of the triangle is 8 cm

Step-by-step explanation:

Area of a triangle(A) is given by:

$A =\frac{1}{2}b \cdot h$           ....[1]

where b is the base and h is the height of the triangle respectively.

As per the statement:

the height of a triangle is 7 cm longer than its base.

⇒$h = b+7$

It is also given that: The area of the triangle is 60 cm²

⇒$A = 60$ cm²

Substitute the given values in [1] we have;

$60 = \frac{1}{2}b \cdot(b+7)$

Multiply both sides by 2 we have;

$120 = b(b+7)$

or

$b^2+7b =120$

⇒$b^2+7b-120=0$

Now factorize this equations:

$b^2+15b-8b-120=0$

⇒$b(b+15)-8(b+15)=0$

⇒$(b-8)(b+15)=0$

By zero product property we have;

b-8 = 0 and b+15 = 0

⇒b = 8 and b = -15

Since, the base of the triangle cannot be in negative.

⇒b = 8 cm

Therefore, the base of the triangle is 8 cm

Answer 2

Base is 8cm, and height is 15 cm