Answer:
a) A =( x^2 -4x)/2
b) 16 cm^2
Step-by-step explanation:
Let the base of the triangle be x cm
since it is longer, then the height would be (x-4) cm
Mathematically, the area of a triangle is the product of the base and the height divided by 2
So, we have this as;
A = 1/2(x-4)x
A = x(x-4)/2
A = (x^2 - 4x)/2
A =( x^2 -4x)/2
To find the area, we only need to substitute 8 cm for x
we have this as;
A = (8^2 -4(8))/2
A = (64-32)/2 = 32/2 = 16 cm^2
We will begin by converting the word problem to relatable mathematical expression in the first part, in the second part, we will substitute for x and find the area which is 48cm^2
Given data
Let the height be x cm
and let the base be y cm
Going by the word problem statement "base that is 4cm longer than its height."
y = x+4
a. the polynomial expression for the area of the triangle is
We know that the area of triangle is given as
Area = 1/2*Base*Height
Area = 1/2*(x+4)*x
Area = 1/2*x^2+4x
Simplify
Area = x^2/2 + 2x
b. The Area when the height is 8cm
We will substitute x= 8cm
Area = (8)^2/2 + 2(8)
Area = 64/2 + 16
Area = 32+16
Area = 48 cm^2
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