# Geometric problems?

show the solution too.

1. half the perimeter of a rectangle is 51cm. if the difference between the length and the width is 13cm. find the area of rectangle.

2. the perimeter of an isosceles triangle is 48 inches. the length of the base is 1 inch less than half the length of one of the 2 equal sides. find the lengths of the sides of the triangle.

THANK YOU

Favorite Answer

let width = x – 13

x + x – 13 = 51 since 51 is half of the perimeter.

2x – 13 = 51 combine like terms

2x = 64 at 13 to both sides

x = 32 divide both sides by 2

Therefore your length equals 32cm and the width equals 19cm.

A = lw

A = 32(19)

A = 608 sq. cm

2) let x = each equal side of isosceles triangle

let 0.5x – 1 = the base

x + x + (0.5x – 1) = 48

2.5x – 1 = 48 combine like terms

2.5x = 49 add 1 to both sides

x = 19.6 divide both sides by 2.5

Each equal side of the isosceles triangle measures 19.6in and the base equals 8.8in.

(the length) + (the width)= 51 cm

(the length) – (the width) = 13 â (the length) = 13 + 13 + (the width) â [13 + (the width)+ (the width)]=51 â

2(the wide)=51-13 â the wide = 19

The length = 51 – ( the wide) â the length = 51- 19= 32

P=51*2=102cm

P= 2( l+b)

l-w=13

l=13+w

Substitue 13+w for l

102= 2((13+w)+w)

Solve the equation for w then whatever value you get for w subtitute it in l=13+w to find l

2)

P=48

Length of base: (1-1/2x)

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

Solve the equation for x (2 sides of the triangle) then for the 3rd side use this 1-1/2x

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