## Phil’s shadow is half as long as Phil is tall. If he were 4 inches taller and his shadow were 3 inches shorter, his height times

Question

Phil’s shadow is half as long as Phil is tall. If he were 4 inches taller and his shadow were 3 inches

shorter, his height times his shadow’s length would be 100 square inches. How tall is Phil? How

in progress 0
2 days 2021-10-12T11:30:20+00:00 1 Answer 0

1. Phil is 16 inches tall and his shadow is 8 inches tall

Step-by-step explanation:

this is an algebra word problem.

1. Find the unknown and label it x.

Let Phil’s shadow be x inches.

2. find other unknown quantities and define them with

Phil’s height= 2x (phil is shadow is half as long as Phil is tall)

3. FInd the equation

if he was 4 inches taller (2x+4)

and his shadow was three inches shorter (x-3)

his height ( 2x+4) times the shadow’s height (x-3) would be 100 square inches.

(2x+4) ×(x-3)=100

(2x+4)(x-3)=100

this is a quadratic equation and there are a number of ways to solve these. the two main ways are

2. expanding and factorising

3. graphing

we will use 2. expanding and factorising for this problem. We need to make the right hand side = 0 by first factorising then rearranging.

(2x*x)+(2x*-3)+(x*4) +(4*-3)=100

2x^2 -6x+4x-3x-12=100

2x^2 -2x=112

2x^2 -2x-112=0

once factorised take out the common factor of 2

2(x^2-x-56)=0

now factorise what’s in the brackets ( two numbers multiply to make 56 but add to make -1.

2(x-8)(x+7)=0

x-8=0 =>   x=8

x+7=0        x=-7 not possible

the shadow is 8 inces long. Phil is 16 inches tall.

Hope this is of help 🙂