Question

The height of a triangle is 4 m less than its base. The area of the triangle is 48 m^2. Find the length of the base.

Answer 1

a 7 m
b 8 m
c 11 m
d 12 m

Answer 2

let the base is=x

Answer 3

so the height is=x-4

Answer 4

the area of a triangle is
1/2(x)(x-4)=48

Answer 5

area of a triangle is
=(1/2)*base*height

Answer 6

There are a couple of ways to do this.

Method 1:

New width = 12+x
New length = 14+x
New area = 255

(12+x) (14+x) = 255
x^2 + 26x + 168 = 255
x^2 + 26x − 87 = 0
(x + 29) (x − 3) = 0, with x > 0
x = 3

New width = 12+3 = 15 m


Method 2:

Length is 2 more than width. If we add same amount to both, then length is still 2 more than width.
w = width of larger garden
w+2 = length of larger garden

w (w+2) = 255
w^2 + 2w − 255 = 0
(w + 17) (w − 15) = 0, with w > 0
w = 15

New width = 15 m

Answer 7

@onlymath r u right with ur solution

Answer 8

I'm not sure what happened up there? but shamim's method was good...

1/2(x)(x - 4) = 48

Lets multiply everything by 2 to cancel out that 1/2

x(x - 4) = 96

Distribute the 'x'

x^2 - 4x = 96

Now we can either plug that into the quadratic formula or just factor it...looks like factoring would be easy enough so

x^2 - 4x - 96 = 0

a * b = -96
a + b = -4

Looks like the 2 numbers that multiply to make -96 AND add to make -4 are \(\large \space 12 \space \text{and} \space 8\)


(x -12)(x + 8)

So it looks like x will be either 12 or -8 (but we know it cannot be -8 ...so we arrive at 12 for your answer