Question

Here are two rectangles.

EH = 10 cm
BC = EF
The perimeter of ABCD is 25 cm.
The area of EFGH is 35 cm²
Find the length of AB.
Optional working

Answer 1

9cm

Explanation:

To find the length of AB, we can use the following information:

• The perimeter of ABCD is 25 cm.
• The area of EFGH is 35 cm².

We can see that the perimeter of ABCD is equal to the sum of the lengths of AB, BC, CD, and DA. We can also see that the area of EFGH is equal to the length of EH times the length of GH.

Perimeter of ABCD:

25 cm = AB + BC + CD + DA

Area of EFGH:

35 cm² = EH × GH

We are given that the area of EFGH is 35 cm², so we can substitute this value into the equation:

35 cm² = EH × GH

We are also given that EH is equal to 10 cm, so we can substitute this value into the equation:

35 cm² = 10 cm × GH

We can now divide both sides by 10 cm to get:

GH = 3.5 cm

EF = 3.5 cm

So,

BC = 3.5 cm

AD = 3.5 cm

We can now substitute the value of GH into the equation for the perimeter of ABCD:

25 cm = AB + BC + CD + DA

We are also given that the perimeter of ABCD is 25 cm, so we can substitute this value into the equation:

25 cm = AB + 3.5cm + CD + 3.5 cm

We can now combine like terms:

25 cm = AB + CD + 7 cm

Since CD = AB (opposite side of rectangle are equal.)

25 - 7 cm = AB + AB

18 cm = 2 AB

We can divide both sides by 2 to get:

`\sf (18 )/(2)cm =( 2 AB)/(2)`

AB = 9 cm

Therefore, the length of AB is 9 cm.