Answer:
the base of the triangle is 8 cm
Step-by-step explanation:
Area of a triangle(A) is given by:
[tex]A =\frac{1}{2}b \cdot h[/tex] ....[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.
⇒[tex]h = b+7[/tex]
It is also given that: The area of the triangle is 60 cm²
⇒[tex]A = 60[/tex] cm²
Substitute the given values in [1] we have;
[tex]60 = \frac{1}{2}b \cdot(b+7)[/tex]
Multiply both sides by 2 we have;
[tex]120 = b(b+7)[/tex]
or
[tex]b^2+7b =120[/tex]
⇒[tex]b^2+7b-120=0[/tex]
Now factorize this equations:
[tex]b^2+15b-8b-120=0[/tex]
⇒[tex]b(b+15)-8(b+15)=0[/tex]
⇒[tex](b-8)(b+15)=0[/tex]
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
