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erma4kov [3.2K]
2 years ago
5

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?

Mathematics
2 answers:
PilotLPTM [1.2K]2 years ago
8 0

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

Digiron [165]2 years ago
4 0
Base is 8cm, and height is 15 cm
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