Question

The height of a photograph is 40 cm greater than the width, and the area of the photograph is 896 cm2what is the height of the photograph?

Answer 1

Answer:

Height = 56 cm

Step-by-step explanation:  

let the width of photograph  be = 'w' cm

let the Height of photograph be = 'h' cm

Now it is given that height is 40 cm greater than width

=> h = w + 40 cm.............................(i)

Now it is given that area of photograph = $896cm^{2}$

We know that area = $Width^{}$x$Height^{}$

Thus we have $h^{}$ x $w^{}$=$896cm^{2}$

Applying value of 'h' from equation i we get

$(w+40^{})$x$w^{}$=$896cm^{2}$

$w^{2} +40w=896cm^{2}$

This is a quadratic equation in 'w' whose solution in standard form is given by

w=$\frac{-b\mp\sqrt{b^{2}-4ac}}{2a}$

upon comparing with standard equation  we see that

a =1

b=40

c=896

applying values in the formula we get

w=$\frac{-40\mp\sqrt{40^{2}-4\times 1\times- 896}}{2 \times1 }$

w1 = 16 cm

w2 = -56 cm

We discard -56 cm since length cannot be negative thus

width = 16 cm

Height = 40+16 cm = 56 cm