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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

7. Scale Drawings and Models

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Exercise 36 Page 605

The long and short sides of a rectangle are congruent.

10 or 26

Practice makes perfect

Let's analyze the given quadrilateral to find the length JK. Keep in mind, we have been told that the figure is a rectangle.

Since the given figure is a rectangle, the short and long sides are congruent. NJ=MK and NM=JK We can use this fact to rewrite the above equation for the long sides in terms of the given expressions, NM=8x-14 and JK=x^2+1.

NM=JK

▼

Solve for x

NM= 8x-14, JK= x^2+1

8x-14= x^2+1

LHS-8x=RHS-8x

- 14 = x^2-8x+1

LHS+14=RHS+14

0= x^2-8x+15

Rearrange equation

x^2-8x+15 = 0

Write as a difference

x^2-3x-5x+15 = 0

Factor out x

x(x-3)-5x+15 = 0

Factor out - 5

x(x-3)-5(x-3) = 0

Factor out (x-3)

(x-5)(x-3) = 0

Use the Zero Product Property

lx-5=0 x-3=0

(I): LHS+5=RHS+5

lx=5 x-3=0

(II): LHS+3=RHS+3

lx=5 x=3

We found that either x=3 or x=5. Let's substitute these values into the expressions for the lengths.

x=3		x=5
Substitution	Simplify	Substitution	Simplify
8( 3)-14	10	8( 5)-14	26
3^2+1	10	5^2+1	26

As we can see, both values of x give us reasonable lengths of the sides. Therefore, JK=10 or JK=26.

Subchapter links

Exercises p.602-605