The base of a triangle is 7cm greater than the height. The area is 60 cm^2.?

Question

Find the height and length of the base.

Answer 1

Let height = h
Base = h + 7
60 = ( 1/2 ) ( h ) ( h + 7 )
120 = h ² + 7 h
h ² + 7 h - 120 = 0
( h + 15 ) ( h - 8 ) = 0
h = 8
Height = 8 cm
Base = 15 cm

Answer 2

enable's say "x" is the top of our triangle. understanding the formulation for the component to a triangle (b/2)*h (a million/2 the backside greater by ability of the top; all of us be attentive to right here: (x + 7)/2)*x = 60 increasing the brackets provides the equation x^2 + 7x - a hundred and twenty = 0 A quadratic equation. Factorising this equation provides: (x + 15)(x - 8) = 0 consequently x = -15 and x = 8 As a length can't be destructive the top of the triangle must be 8. consequently top of the triangle = 8cm and the backside = 8 + 7 = 15cm. top = 8cm Base = 15cm

Answer 3

A = 1/2(BH)
So 2a = bh
120 = x(x + 7)
x² + 7x - 120 = 0
(x - 8)(x + 15) = 0
x = 8 = height (The negative root of -15 makes no sense here)
So base = 8 + 7 = 15

Check : A = 1/2 (bh)
60 = 1/2 (15)(8)
60 = 1/2 (120)
60 = 60

Answer 4

A = bh/2

h = height of a triangle
b = h + 7

60 = h(h + 7)/2
120 = h^2 + 7h
0 = h^2 + 7h - 120
0 = (h - 8)(h + 15)
h = {8, -15}

You know that a negative value makes no sense here so height is 8 cm and base is 15 cm.

Answer 5

60=1/2(7+x)(x)

if 1/2 of (7+x)(x) equals 60, then 60*2=(7+x)(x)

60*2= 120

120=(7+x)(x)

is it 10? 120=(7+10)(10)
120=(17)(10) 17*10=170. NO

smaller than 10....9?

120=(7+9)(9)
120=(16)(9) 16*9=144 NO

smaller than 9....8?

120=(7+8)(8)
120=(15)(8) 15*8=120 YES

the height is 8cm, the base is 15cm.

your welcome!!!

Answer 6

h = height
l = lenght
a = area

a = (hl)/2

h = x
l = x + 7

therefore
(x * (x + 7))/2 = 60
(x^2 + 7x)/2 = 60
x^2 + 7x = 120

Using the quadratic equation

x = ((-7+or- sqrt (7^2-(4*1*120))/2*1
x = 8 or -15

you can't have a negative lenght so x =8

so you have a height of 8
and a lenght of 15

Answer 7

Area of triangle = bh/2
b = h+7

(h+7)h/2 = 60
(h+7)h = 120
h² + 7h - 120 = 0
h² - 8h + 15h - 60 = 0
h(h-8)+15(h-8) = 0
(h+15)(h-8) = 0
h = {-15, 8}

h must be positive
h = 8cm
b = 8+7=15cm

Answer 8

let height be x cm...

are of triangle =1/2 (x)(x+7)=60
x^2+7x-120=0
(x+15)(x-8)=0
x=-15 x=8

height =8cm (reject -15 cos it is not possible)
base=15cm