A. Refer to trapezoid EFGH with median I)
1. If IJ = x, HG = 8 and EF = 12,
what is the value of x?
2. If IJ = y + 3, HG = 14 and EF = 18,
what is the value of y? What is IJ?
3. If HG=x, IJ = 16 and EF = 22,
what is value of x?
4. If HG= y-2, IJ = 20 and EF = 31, what is the value of y? What is HG?
5. If HI = 10 and IE= x-4, what is the value of x? What is IE?
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Answers
Concept used :- The line segment joining the midpoints of the non parallel sides of a trapezium is equal to half of the sum of the lengths of the parallel sides .
so,
- IJ = (HG + EF)/2 .
1. If IJ = x, HG = 8 and EF = 12, what is the value of x ?
Answer :-
→ IJ = (HG + EF)/2
→ x = (8 + 12)/2
→ x = 20/2
→ x = 10 .
2. If IJ = y + 3, HG = 14 and EF = 18, what is the value of y ? What is IJ ?
Answer :-
→ IJ = (HG + EF)/2
→ (y + 3) = (14 + 18)/2
→ (y + 3) = 32/2
→ (y + 3) = 16 = IJ .
→ y = 16 - 3
→ y = 13 .
3. If HG = x, IJ = 16 and EF = 22, what is value of x ?
Answer :-
→ IJ = (HG + EF)/2
→ 16 = (x + 22)/2
→ 16 * 2 = x + 22
→ 32 = x + 22
→ x = 32 - 22
→ x = 10 .
4. If HG= y-2, IJ = 20 and EF = 31, what is the value of y ? What is HG ?
Answer :-
→ IJ = (HG + EF)/2
→ 20 = (y - 2 + 31)/2
→ 20*2 = y + 29
→ 40 = y + 29
→ y = 40 - 29
→ y = 11 .
then,
→ HG = y - 2 = 11 - 2 = 9 .
5. If HI = 10 and IE= x-4, what is the value of x ? What is IE ?
Answer :-
→ HI = IE { since I is mid point .}
→ 10 = x - 4
→ x = 10 + 4
→ x = 14 .
then,
→ IE = x - 4 = 14 - 4 = 10 .
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