Answer:
height is 21cm and the base is 14cm
Step-by-step explanation:
Take a look at the equation for the area of a triangle [tex]A = \frac{bh}{2}[/tex]
Write "height of a triangle is 7 cm greater than the base" as an equation:
h = b + 7
Substitute h and the area of the triangle, 147 into the equation for area.
[tex]A = \frac{bh}{2}[/tex]
[tex]147 = \frac{b(b+7)}{2}[/tex] distribute over brackets
[tex]147 = \frac{b²+7b)}{2}[/tex] get rid of fractions
[tex]147*2 = b²+7b[/tex]
[tex]294 = b²+7b[/tex]
Rearrange to standard for for quadratic equations
0 = b²+7b - 294
standard form is 0 = ax² + bx + c
In this base, the x variable is replaced by "b".
Use the quadratic formula to solve for b. Substitute the other three values.
[tex]x = \frac{-b ±\sqrt{b^{2}-4ac} }{2a}[/tex]
[tex]x = \frac{-(7) ±\sqrt{7^{2}-4(1)(-294)} }{2(1)}[/tex] Simplify
[tex]x = \frac{-7 ±\sqrt{1225} }{2}[/tex]
[tex]x = \frac{-7 ±35 }{2}[/tex]
Split the equation at ±
[tex]x = \frac{-7 +35 }{2}[/tex]
[tex]x = \frac{28}{2}[/tex]
[tex]x = 14[/tex] <=base
[tex]x = \frac{-7 -35 }{2}[/tex]
[tex]x = \frac{-42}{2}[/tex]
[tex]x = -21[/tex] <=We know this number is not possible, so its inadmissible.
The base is 14 cm.
Substitute base = 14 in h = b + 7
h = b + 7
h = 14 + 7
h = 21
The height is 21cm.
Therefore, the height is 21cm and the base is 14cm.
