Answer:
length of the base = 5cm , height = 6cm
Step-by-step explanation:
Let the length of it's base be x , since the height of a triangle is 4cm less than twice the length of its base,
twice it's base = 2x
Therefore , the height = 2x - 4
Area = 15[tex]cm^{2}[/tex]
The formula for finding the area of a rectangle is given as :
Area = [tex]\frac{1}{2}[/tex] x base x height
Therefore:
15 = [tex]\frac{1}{2}[/tex] x [tex]x[/tex] x [tex]2x - 4[/tex]
[tex]15 = x^{2} - 2x[/tex]
therefore :
[tex]x^{2} -2x-15 = 0[/tex]
factorizing , we have
[tex](x-5)(x+3) = 0[/tex]
which means that
[tex]x = 5[/tex] or [tex]-3[/tex]
since the length of the base can not be negative , then , the length of the base is 5 cm
height = 2(5) - 4
height = 10 - 4
height = 6
