Question

pls answer with an explanation

Answer 1

Answer:

hey your answer is as follows

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Step-by-step explanation:

now let the required trapezium be abcd

wherein bc and ad are two parallel sides ie requied bases of it such that bc is longer base and ad is shorter base.

also ab is its height such that ab perpendicular to bc and ad ie angle abc and angle bad are 90 degree each

so according to first condition

bc=5ad (1)

according to the second condition

ab=ad-1 (2)

so here area of trapezoid=90 unit.square

so we know that

area of trapezoid=1/2×[sum of length of parallel sides]×height

thus 90=1/2×(bc+ad)×ab

=1/2×(5ad+ad)×(ad-1) from (1) and (2)

=6ad(ad-1)/2

=6ad square-6ad/2

ie 6ad square-6ad=180

so dividing by 3 on both sides

we get

ad square-ad=30

so ad square-ad-30=0

ie ad square-6ad+5ad-30=0

so ad(ad-6)+5(ad-6)=0

ie (ad-6)(ad+5)=0

so ad=6 or ad=-5

but as dimensions length of any geometric figure are never negative

ad=-5 is absurd

thus ad=6 units

so substitute value of ad in (1) and (2)

we get bc=30

ab=5

hence length of shorter base is 6 units